PhD position is available in the area of graphical models at Nanyang Technological University, Singapore.

Students with solid training in applied mathematics or statistics are especially encouraged to apply.

Project description:

Graphical models, referred to in various guises as "Markov random fields," "Bayesian networks," or "factor graphs," provide a statistical framework to encapsulate our knowledge of a system and to extract information from incomplete data. With carefully chosen assumptions (e.g., conditional independence of selected random variables), graphical models can be used to derive highly efficient techniques for data analysis; the main idea is to exploit the (existing or imposed) structure in the statistical model. However, graphical models are at present mostly limited to Gaussian or discrete random variables, while many real-life statistical problems involve non-Gaussian random variables. For example, this is the case of all positive quantities (amplitude, energy, magnitude), which are commonplace in physics and earth sciences. Moreover, extreme events such as earthquakes, hurricanes and floods, which are of special interest in natural hazards and risk an alysis, cannot be described accurately by means of Gaussian distributions. Consequently, there is a tremendous need for new types of graphical models for dealing with non-Gaussian data. Such graphical models would enable us to solve large-scale real-life inference problems efficiently, while relaxing many simplifying assumptions about the data, and allowing us to better quantify uncertainties and trade-offs in model parameters.

To move toward this goal, we will integrate copula theory in the framework of graphical models. Statistical copulas enable us to tie any kind of marginal distributions (Gaussian, non-Gaussian and even non-parametric) together to form a joint distribution. Through the language of graphical models, we will impose structure on the resulting non-Gaussian joint distributions, so that they can describe the relationship between thousands or even millions of non-Gaussian random variables in an accurate and compact manner. By exploiting the structure in those high-dimensional statistical models, we will derive highly efficient algorithms for i) learning model parameters; ii) imputing missing data; iii) extrapolation; iv) conditional simulation; v) forecasting; vi) other important statistical tasks. We will derive statistical performance guarantees for those learning and inference algorithms. We will then apply the proposed models to several important problems in earth sciences. We will consi der copula graphical models for both "nominal" (non-extremal) data and for extreme events.